Special Issue on
Theory, Methods, and Applications of Fractional Calculus in Engineering and Other Sciences

In the present era, fractional calculus plays an important role in various fields. Fractional Calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators in much the same way fractional exponents is an outgrowth of exponents with integer value.

Based on the wide applications in engineering and sciences such as physics, mechanics, chemistry, and biology, research on fractional ordinary or partial differential equations and other relative topics is active and extensive around the world. In the past few years, the increase of the subject is witnessed by hundreds of research papers, several monographs, and many international conferences.

This special issue will be a devoted topic to high current interest falling within the scope of the Journal and will attract many papers of the highest quality. The objective of this special issue is to highlight the importance of fractional operators and their applications and let the readers of this journal know about the possibilities of this new tool and to provide a multidisciplinary forum of discussions among scientists who have been interested in investigating diverse branches related to fractional calculus and applying theories of fractional calculus to their diverse research areas. This issue is expected to welcome articles of significant and original results and survey articles of exceptional merit, which are closely related to fractional calculus in either theoretical or applicative sense.

About the issue

The scope of topics covered in the this issue include:

Mathematical analysis of fractional calculus operators,

Optimization techniques and their applications

Fractional integral inequalities and their q-analogues

Various inequalities involving the fractional integral and differential operators and so on

Mathematical analysis of fractional theoretical models

New methods for solving fractional differential equations

Applications of fractional operators, including fractional models

Controllability of fractional systems of differential equations or numerical methods applied to the solutions of fractional differential equations applications in physics, mechanics, and so forth

Special Issue on
Application and Future Scope of Fundamental Mathematical and Computational Sciences in Engineering & Technology

Fundamental mathematics and statistics are used by the great majority of the workforce, without their thinking of themselves in any way as mathematicians or statisticians. Recent study of Massey University estimated that more than 85% of the New Zealand work force is involved in simple forms of measurement and estimation, more than 67% is involved in some form of data collection and interpretation, and over 50% is responsible for some form of inventory or money management. Similar data can be found in other Asian, European and African countries of the world. Usually, the mathematical activity is restricted to well-defined tasks - computations, measurements, plotting and interpretation of simple graphs - carried out on a routine basis, without the person doing the work being able easily to modify their task in response to changing circumstances. Most of the tasks would be within the scope of the regular school programme. There is then a very wide spectrum of mathematical tasks embedded into different professional fields, for example, finance and accounting, engineering science and architecture technology, business and management, agriculture, medicine, physical, biological and social sciences, etc. Almost universally, the computations for these tasks are no longer handled manually, but are coded into different types of software - spreadsheets, statistical packages, purpose-built packages for computer-aided design, inventory control, forecasting etc. The mathematical skills are required not in operating the computer terminal, but in interpreting the output, checking that requirements on input data are properly satisfied, understanding the things that can go wrong, adapting the use of the software to the particular requirements of the problem at hand. At the less mathematical end of the spectrum, the persons undertaking these tasks may not be easily able updating the procedures they use to cope with new or changing circumstances. At the more mathematical end, the persons may spend much of their time developing such modifications or guiding and advising less confident staff. As in any professional task in the field of medical science, agricultural science, engineering science and technology, the value and quality of the service provided depends greatly on the quality of the evaluator/estimator and the perspective they are able to bring to the problem as a result of their background knowledge and experience. In this respect, the mathematical training of the staff concerned may vary from, at the lower end, a university service course on basic mathematics or statistics, topped up by specific applications courses in the subject area, to, at the upper end, a full masters degree or higher in one of the mathematical sciences.

Finally, there is a logical consistency in which virtually all major scientific and technological advances have required appropriate mathematical tools or theories for their development. At some stage, these tools or theories were themselves the subject of independent mathematical research.

It is highly expected that the information and exploration of significant results gained through the present special issue will contribute to the world economy, and the following factors likely to affect their role in the future:

• The most important role of mathematics is in underpinning almost all activities in a modern society of science & technology. It operates at many levels and extends across all socio-economic sectors.

• To find a high general level of quantitative literacy; care for data quality and integrity in both public and private sectors;

• To find adequate mathematical expertise available for proper advice and interpretation of quantitative software, and the development, interpretation, and application of quantitative models;

• To recognize that proper uses of computer software and packages for complex or high-consequence analyses requires sound professional kn